It's fine the way it is. In a conversation, we would usually say "Most of the time, we walked." How did you get up the mountain? Did you take the cable car? No, we went on foot. We walked up.

If you want an answer according to writing style, the answer is, "Most of the time, we travel by foot". This is the common phrase. However, according to grammar rules, it can also be said using the preposition "on foot".